Turn pump and output readings into clear efficiency. See thresholds, quantum limits, and losses instantly. Download tables, share reports, and tune your laser setup.
Slope efficiency describes how output power increases with pump power in the linear region above threshold.
| Point | Pump power (W) | Output power (W) | Notes |
|---|---|---|---|
| 1 | 5.0 | 1.2 | Above threshold, stable operation |
| 2 | 7.0 | 2.3 | Within linear region, same alignment |
| Threshold | 3.5 | 0.0 | Estimated from L-I intercept |
Slope efficiency describes the incremental conversion from pump power to laser output power in the near-linear region of the L-I curve. It is written as dPout/dPin (often in W/W). This differs from simple power conversion at one point, because it focuses on how performance changes as you increase pump.
Use operating points safely above threshold where output grows approximately linearly with pump. Keep alignment, temperature, drive conditions, and cavity settings unchanged between points. Avoid thermal roll-over, gain saturation, or clipping, because those effects reduce linearity and can make the extracted slope misleading.
Real devices vary widely. Edge-emitting diode lasers commonly show slope efficiencies around 0.3–0.8 W/W depending on wavelength and packaging. Diode-pumped solid-state systems are often lower (roughly 0.1–0.3 W/W optical-to-optical) due to quantum defect and intracavity losses. Well-designed fiber lasers can exceed 0.6 W/W optical-to-optical under efficient pumping.
The threshold pump power Pth is where lasing begins. The threshold-based method uses ηs = Pout/(Pin−Pth). If you only have two points, the calculator estimates Pth from the line passing through your data. A negative estimated threshold usually indicates points below threshold, nonlinearity, or inconsistent readings.
If only a fraction A of pump is absorbed, the absorbed slope efficiency is higher: ηs,abs ≈ ηs/A. Adding pump and laser wavelengths enables a quantum-limit check using λp/λl. The calculator also estimates differential quantum efficiency ηq ≈ ηs·(λl/λp), which helps separate optical losses from photon-conversion limits.
Power meters and calibration can introduce ±1–3% uncertainty or more. The optional uncertainty field applies a simple propagation model to show an approximate 1σ slope uncertainty. Uncertainty grows quickly when your two pump points are too close together, so increasing the separation between points (while staying in the linear region) improves confidence.
Once you have ηs and Pth, output can be approximated as Pout ≈ ηs·(Pin−Pth). For example, if ηs = 0.55 and Pth = 3.5 W, then at Pin = 8 W the prediction is about 0.55·(8−3.5)=2.48 W, assuming the same linear regime.
Improve mode overlap between pump and gain, reduce passive losses (clean optics, proper coatings, low-loss fiber splices), optimize output coupling, and manage temperature to avoid roll-over. Stable alignment and a well-matched pump wavelength can significantly increase usable slope efficiency, especially in systems limited by thermal lensing or absorption mismatch.
Slope efficiency is the incremental change in output with pump above threshold. Pout/Pin is a point efficiency at a specific operating condition and includes threshold overhead and nonlinearity.
Values above 1 usually indicate inconsistent units, measurement errors, or points not in the same regime. For optical pumping, a simple wavelength ratio check helps flag unrealistic slopes.
Negative slope typically comes from swapped points, operation in roll-over or saturation, or noisy measurements. Re-measure in a stable linear region above threshold and keep conditions constant.
Use two-point when you have two reliable linear-region points. Use threshold-based when you have a trusted threshold from a fit to several L-I data points.
Yes, if you use consistent average powers and remain in a comparable operating regime. For strongly nonlinear pulsed behavior, consider analyzing pulse energy versus pump and fitting only the linear portion.
Absorption fraction estimates how much of the pump is actually absorbed in the gain medium. If absorption is less than 1, absorbed slope efficiency can be higher than the measured slope versus incident pump.
Wavelengths enable a quick quantum-limit check using λp/λl and an estimate of differential quantum efficiency. These help interpret whether losses, quantum defect, or measurement issues dominate the result.